In the new prior distribution we use a combination of Tikhonov and Phillips-Twomey-regularization both in the real and imaginary parts. Here we apply a small amount of Tikhonov-regularization by setting \(\rho = 10^{-8}\) , such that the resulting regularization operator gets regular. This means that the regularized regression problem (REF ) can be transformed into standard Tikhonov form and that the monotonicity results from [1]} are still valid. Each second finite difference is clearly a function of three neighboring points, therefore a decoupled computation of the joint MAP-estimator
\(x^{1}_{opt}, ..., x^{s}_{opt} := \underset{x^{1}, ..., x^{s}}{\mathrm {argmax}}\;p(x^{1}, ..., x^{s} | e^{1}, ..., e^{s})\) 
